How a nerve fires, written as equations. Hodgkin and Huxley probed a squid’s giant axon and found the action potential: voltage-gated sodium channels open, sodium rushes in, the membrane depolarizes, which opens more channels — a regenerative surge — then potassium channels open to reset it. The result is all-or-nothing: below threshold, nothing; above it, a full spike, every time. The 1952 model that turned the mind into biophysics.
THE TECHNIQUE threshold → all-or-nothing spike
The demo shows the all-or-nothing threshold and the regenerative sodium feedback: live demo
HISTORY & CREDIT Hodgkin & Huxley · 1952
“A stronger stimulus makes a bigger spike.” — above threshold every spike is the same size; strength is coded in the rate of firing, not the height. cited
the surge · depolarization opens Na⁺ channels, which depolarize further — regenerative positive feedback. all-or-nothing · cross threshold → full spike; below → silence; K⁺ resets. 1952 · Alan Hodgkin & Andrew Huxley, the squid giant axon (Nobel 1963).
A thought, as a threshold crossing. biophysics
RECOMMEND FOR I-13 the threshold, on the compiler
On i-13, 50mV gives no spike, 60mV gives a full spike, and sodium feedback is regenerative:
$ i13 run lf_hodgkin-huxley.i13
RUN OK · 46 step(s)
sub(50) = 0 supra(60) = 100
all_or_nothing = 1 regenerative = 1
Recommend as a NULL — a threshold nonlinearity (B39). The all-or-nothing response is a pinned function of the voltage and threshold; the regenerative feedback is dynamics, not a same-function DOF. NULL — the spark of a thought.